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Time-Consistent Investment-Reinsurance Strategies for the Insurer and the Reinsurer under the Generalized Mean-Variance Criteria

Author

Listed:
  • Helu Xiao

    (School of Business, Hunan Normal University, Changsha 410081, China)

  • Tiantian Ren

    (School of Business Administration, Hunan University, Changsha 410082, China)

  • Yanfei Bai

    (School of Business Administration, Hunan University, Changsha 410082, China)

  • Zhongbao Zhou

    (School of Business Administration, Hunan University, Changsha 410082, China)

Abstract

Most of the existing literature on optimal investment-reinsurance only studies from the perspective of insurers and also treats the investment-reinsurance decision as a continuous process. However, in practice, the benefits of reinsurers cannot be ignored, nor can decision-makers engage in continuous trading. Under the discrete-time framework, we first propose a multi-period investment-reinsurance optimization problem considering the joint interests of the insurer and the reinsurer, among which their performance is measured by two generalized mean-variance criteria. We derive the time-consistent investment-reinsurance strategies for the proposed model by maximizing the weighted sum of the insurer’s and the reinsurer’s mean-variance objectives. We discuss the time-consistent investment-reinsurance strategies under two special premium principles. Finally, we provide some numerical simulations to show the impact of the intertemporal restrictions on the time-consistent investment-reinsurance strategies. These results indicate that the intertemporal restrictions will urge the insurer and the reinsurer to shrink the position invested in the risky asset; however, for the time-consistent reinsurance strategy, the impact of the intertemporal restrictions depends on who is the leader in the proposed model.

Suggested Citation

  • Helu Xiao & Tiantian Ren & Yanfei Bai & Zhongbao Zhou, 2019. "Time-Consistent Investment-Reinsurance Strategies for the Insurer and the Reinsurer under the Generalized Mean-Variance Criteria," Mathematics, MDPI, vol. 7(9), pages 1-25, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:857-:d:268040
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    References listed on IDEAS

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    1. Zhu, Huiming & Deng, Chao & Yue, Shengjie & Deng, Yingchun, 2015. "Optimal reinsurance and investment problem for an insurer with counterparty risk," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 242-254.
    2. Zeng, Yan & Li, Zhongfei, 2011. "Optimal time-consistent investment and reinsurance policies for mean-variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 145-154, July.
    3. Tomas Björk & Agatha Murgoci, 2014. "A theory of Markovian time-inconsistent stochastic control in discrete time," Finance and Stochastics, Springer, vol. 18(3), pages 545-592, July.
    4. Wu, Huiling & Zeng, Yan, 2015. "Equilibrium investment strategy for defined-contribution pension schemes with generalized mean–variance criterion and mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 396-408.
    5. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    6. Zhou, Zhongbao & Xiao, Helu & Yin, Jialing & Zeng, Ximei & Lin, Ling, 2016. "Pre-commitment vs. time-consistent strategies for the generalized multi-period portfolio optimization with stochastic cash flows," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 187-202.
    7. O. L. V. Costa & R. B. Nabholz, 2007. "Multiperiod Mean-Variance Optimization with Intertemporal Restrictions," Journal of Optimization Theory and Applications, Springer, vol. 134(2), pages 257-274, August.
    8. Jieming Zhou & Xiangqun Yang & Ya Huang, 2017. "Robust optimal investment and proportional reinsurance toward joint interests of the insurer and the reinsurer," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(21), pages 10733-10757, November.
    9. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    10. Waters, Howard R., 1983. "Some mathematical aspects of reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 2(1), pages 17-26, January.
    11. Duni Hu & Hailong Wang, 2018. "Time-consistent investment and reinsurance under relative performance concerns," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(7), pages 1693-1717, April.
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    1. Zilan Liu & Yijun Wang & Ya Huang & Jieming Zhou, 2022. "Optimal Time-Consistent Investment and Premium Control Strategies for Insurers with Constraint under the Heston Model," Mathematics, MDPI, vol. 10(7), pages 1-22, March.

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